Tony wants to save for retirement and is considering the following plan.

Save $$3,000$ today $($period $0)$

Save $$4,000$ per year starting $1$ year from today $($period $1)$ for $5$ years $($last payment made in period $5).$

Save $$5,000$ per year starting one year from today $($period $1)$ for $10$ years $($last payment made in period $10).$

If the interest rate is $4\%,$ which of the following accurately describes the present value of this plan?

Note: You may find it useful to draw a timeline where all cash flows are listed. This may aid you in answering the question.

A$.PV=$$$3,000+$$$4,000(1+0\mathrm{.}04{)}^5+$$$5,000(1+0\mathrm{.}04{)}^{10}$

B$.PV=$$$3,000+\frac{4,000}{(0\mathrm{.}04)}((1+0\mathrm{.}04{)}^5-1)+\frac{\text{\$}5000}{0\mathrm{.}04}((1+0\mathrm{.}04{)}^{10}-1)$

C$.PV=$$$3,000+\frac{\text{\$}4,000}{(1+0\mathrm{.}04{)}^5}+\frac{5000}{(1+0\mathrm{.}04{)}^{10}}$

D$.PV=$$$3,000+\frac{\text{\$}4,000}{0\mathrm{.}04}(1-\frac{1}{(1+0\mathrm{.}04{)}^5})+\frac{\text{\$}5000}{0\mathrm{.}04}(1-\frac{1}{(1+0\mathrm{.}04{)}^{10}})$